Thank you for your question.
If this lady was to obtain a green card through the lottery, she would be able to petition for her spouse to obtain legal status, once her status is cemented. However, whether the petition would be granted would be left up to the discretion of the immigration authorities. If he entered the country illegally and/or has charges pending against him (especially if they are of a serious nature), it is very possible that the immigration authorities will deny any application that is submitted on his behalf, which could ultimately lead to his deportation.
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Good Luck!
Lawyer
My law firm practices immigration law.